"a way of taming uncertainty, of turning raw data into arguments that can resolve profound questions" (Amabile 1989)
Success depends on evaluating the relative support for different models
Last updated: 2017-02-08
"a way of taming uncertainty, of turning raw data into arguments that can resolve profound questions" (Amabile 1989)
Success depends on evaluating the relative support for different models
Do long-winged crickets have a higher resting metabolic rate than short-winged crickets?
Controlling for body mass,
Which set of loci best predicts oil content in corn kernels?
What are the phylogenetic relationships between dog breeds & other canids?
Is this bone more like a chimpanzee, australopith, Neandertal, or modern human?
Do alligators exhibit determinate or indeterminate growth and does growth depend of atmospheric oxygen levels?
Determinate:
Indeterminate:
von Bertalanffy:
\[Femoral~Length\left(Age\right) = \theta_1 \left(1 - e^{-\theta_2 \left(Age - \theta_3\right)}\right)\]
Logistic:
\[Femoral~Length\left(Age\right) = \frac{\theta_1}{1 + e^{\frac{\theta_2 - Age}{\theta_3}}}\]
Polynomial:
\[Femoral~Length\left(Age\right) = a + b \cdot Age + c \cdot Age^2\]
Your Question Here
Algebraic (closed form) solutions for estimating parameters
\[\bar{Y} = \frac{\sum_{i=1}^{n}Y_i}{n}\]
Like the slope in bivariate regression, many are based of sums of squares (summed squared deviations).
\[b = \frac{\sum\left(X_{i}-\bar{X}\right)\left(Y_{i}-\bar{Y}\right)}{\sum\left(X_{i}-\bar{X}\right)^{2}}\]
For a given mean, how likely is observing my data?
Analytical solutions are generally equal to the maximum likelihood solutions (for set of assumptions).
What is the probability of these parameter estimates given the data and my prior knowledge?
\[Pr[\theta | Data] = \frac{Pr[Data | \theta] \times Pr[\theta]}{Pr[Data]}\]
No quiz for this lecture.
Move on to Lecture 04-2.
Amabile, T. 1989. Against All Odds Inside Statistics. Annenberg/CPB Collection; Intellimation [distributor].